Representation theory, geometry and whatever else we decide is worth writing about today.

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Author Archives: Ben Webster

I have the excellent luck to be sending this semester in Paris, thanks to the Fondation Sciences Mathématiques de Paris. Part of the deal is that I’m giving a weekly course at the “graduate level” (though I think I have more professors than graduate students in the course) on higher representation theory. Also thanks to FSMP, the course is being videotaped and posted online; the first installment is up here. I’m also posting the videos and additional commentary on a WordPress site; if you have any questions, you can always ask them there (or here, but maybe it’s more germane there).

Well, from my perspective at least, the conference was a success. We all made it through in one piece, and no one got trapped on the subway. If any of you are looking for the videos of the talks, they can be downloaded from this page. That’s a only a temporary hosting solution, but at least they’re available for the moment.

As those of you who’ve scrolled down the page know, the conference I mentioned a few months ago (now sadly memorializing the life of Andrei Zelevinsky) is starting tomorrow. Of course, for those of you who don’t live in the Boston area, coming to conference isn’t an option unless you were already traveling today, but I do have a (somewhat belated) announcement. Assuming that the AV gods are kind and everything goes as planned, it should be possible to watch the talks live (of course, we’ll also make the videos available after the conference, in case you’re busy). The schedule is here; the talks start at 10am tomorrow.

So, obviously posting on this blog has ebbed a little (I keep hoping to reverse this trend, but I think we’ve all found that demands on our time that come before blog posting tend to ratchet upward, not downward). I assume there are still a few people reading, though, and I wanted to do a little promotion.

One of the thing that’s been demanding my time lately has been conference organization. We’re planning a conference at Northeastern next spring in recognition of the 60th birthday of Andrei Zelevinsky, with the exteremely original name of “Algebra, Combinatorics and Representation Theory”. I think it’s going to be great, and I encourage any of you who are able and interested to attend; we have a really great line-up of speakers.

For more information, see our website. I want to particularly encourage young people to attend; we’re really hoping (cross your fingers) to have funding for grad students and postdocs. (Furthermore, it will help us to obtain said funding if young people express an interest in coming. So, if you would like to come, please register).

This is the title of a fairly interesting paper, the conclusions of which I would summarise as follows: after the collapse of the Soviet Union there was a sudden drop in the number of papers published by Americans working in fields which had been popular in the Soviet Union, which did not happen in fields which were unpopular there. Their papers were also less cited, and they moved to less prestigious institutions. Collaborating with Soviet immigrants afforded some but not total protection from this effect. Remarkably (and not entirely irrelevantly for me; I’m actually a data point in the paper, and my advisor is actually mentioned by name) this effect was transmitted to students: students after the fall of the Soviet Union wrote more (and more cited) papers if their advisor had immigrated to the US than if they had an American advisor who works topics popular among Soviets (with students that had American advisors working in topics unpopular with Soviets were in between).

This is obviously a very crude analysis (for example, “fields” means top level AMS Subject Class groups, which we all know are deeply flawed), but it’s still a very interesting, and to me at least slightly counter-intuitive conclusion. The authors suggest that the immigration of Soviet mathematicians to the US had a slightly negative effect on the number of papers written by all mathematicians in the US (the immigrants didn’t write enough to make up for the drop amongst American authors), which is not at all what I would have expected.

I keep feeling I should comment on the kerfuffle around Tim Gowers and Elsevier. I had some similar thoughts way back when, though I found that I actually did not have the necessary chutzpah to respond to referee requests as I suggested therein. At the moment, I really find myself just wishing I understood the situation better.

On Gower’s blog, we’ve had the response from within Elsevier; I don’t find it particularly convincing, but what do you expect. I don’t think that anyone disagrees that at one point commercial publishers provided a service learned societies didn’t have the resources to provide. I personally think that things have changed to the degree that is false, but I can’t say I’m certain.

What I would really love to hear is the response from someone on the editorial board of an Elsevier journal about why they stay. The editorial boards are really the key to the business of any commercial publisher; the moment they jump ship, there just is no journal. Why didn’t the board of Topology leaving spark a mass wave of resignations? We got a bit of this from Scott Carter on my previous post, but I still don’t entirely understand the situation. So, I have a very serious question for any readers sitting on the board of journals with commercial publishers generally, and Elsevier specifically: what are the publishers providing for you that couldn’t be reproduced by, say, Scholastica? Have you thought about leaving but decided it doesn’t make sense for some reason I don’t see? Or is the situation fine in your opinion?

Sigh. Congress is trying (again) to undermine the NIH’s open access policy. As usual, you should write your congress-critters. You can do that easily from OpenCongress here. My letter is below the fold. Continue reading →

In a comment on my last post, plm suggests that my condition about the rules of turning energy functions into flows be itself time invariant is the only way to justify requiring that symplectic forms be closed.

While I agree that this is a good way of thinking about what closeness is supposed to mean, and maybe the best, I would dispute that it’s the only one. It’s a very reasonable condition from the pure math side as a kind of “flatness.” Continue reading →

I’m teaching a graduate course in symplectic geometry and GIT this semester, and am going to try to produce some posts related to lectures I’m giving there. Hopefully, this will help me think things through and put some new exposition out there on the internet.

So, obviously, the first question is “what is a symplectic manifold?” Now, wikipedia will tell you it’s a manifold equipped with a non-degenerate closed 2-form. Certainly that’s right, but it doesn’t tell a novice in symplectic geometry much. Why think about such a structure?

So let me try to put a different spin on this. This isn’t all that new of a spin (in fact, Henry Cohn wrote almost exactly the same thing here), but I don’t know of anywhere symplectic manifolds are really presented like this: I want to think of a symplectic manifold as a space where one can do a particular flavor of classical mechanics. Continue reading →

Since we’ve already set the precedent that it’s OK to use the blog for job announcements, let me do a little promotion. My current home, Northeastern, has just posted postdoctoral and tenure-track job announcements. If people have questions about either position or life at NU, they are encouraged to email me (though there is a decent chance I’ll just refer you on to the appropriate authorities).

I particularly want to push the postdoctoral position, because, well, first of all I want to have a more talented postdocs around the department (more in number, no insult intended to our currentpostdocs); I’m also on the search committee for the position, so I have some responsibility to my colleagues to find good people to hire.

Furthermore, as we’ve discussed, titles for postdoctoral jobs are generally confusing; what exactly does “Research Instructor” mean? This is going to sound stupid, but it’s right there in the name; you’re supposed to do research and instruct people. We’re looking for people who will do both of those things well. Candidates are expected to be part of the research life of the department, and we are definitely hoping to find people whose interests overlap with faculty members here. We also take the teaching component of the job very seriously, but the teaching load is intended so that you have time to teach your classes well and work on other things; it is below Noah’s magic line at 3 semester courses a year.

Which is all a long way of saying I look forward to seeing your applications.

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Secret Blogging Seminar

A group blog by 8 recent Berkeley mathematics Ph.D.'s. Commentary on our own research, other mathematics pursuits, and whatever else we feel like writing about on any given day. Sort of like a seminar, but with (even) more rude commentary from the audience.